B. L. Alterman & Justin C. Kasper July 18, 2019 Helium Variation Across Two Solar Cycles Reveals A Speed-Dependent Phase Lag B. L. Alterman & Justin C. Kasper July 18, 2019

Solar Wind Helium Abundance & Sunspot Number (SSN) Definitions Published Observations Hydrogen (Protons) 95 % by number density Fully Ionized Helium (Alphas) 4% by number density Helium Abundance 𝐴 𝐻𝑒 =100 × 𝑛 𝛼 / 𝑛 𝑝 𝐴 𝐻𝑒 & SSN Cross Correlation 𝜌( 𝐴 𝐻𝑒 , 𝑆𝑆𝑁) 𝜌( 𝐴 𝐻𝑒 ,𝑆𝑆𝑁) Strongest in slow wind ( 𝑣 𝑠𝑤 ≲ 550 km/s) Falls off for 𝑣 𝑠𝑤 >426 km/s Helium vanishing speed 𝑣 0 =259 km/s Within 1𝜎 of min observed 𝑣 𝑠𝑤 Possibly indicates helium essential to solar wind formation

Data Sources Wind/SWE FCs Solar cycles 23 & 24; end of cycle 22 Solar Wind Ions SSN Wind/SWE FCs Solar cycles 23 & 24; end of cycle 22 > 23 years Covers one Hale cycle Long-term stability of SWE/FC system essential to this study 13 month smoothed SSN Solar Information Data Center (SIDC)

𝐴 𝐻𝑒 ( 𝑣 𝑠𝑤 , 𝑡) & SSN Trailing end of cycle 22 through decline of cycle 24. SSN in black, dashed 𝐴 𝐻𝑒 𝑣 𝑠𝑤 ,𝑡 colored lines. 10 𝑣 𝑠𝑤 quantiles Color & symbol Covers 312 km/s to 574 km/s Take 250 day averages of all data Legend 𝑣 𝑠𝑤 −𝜌( 𝐴 𝐻𝑒 ,𝑆𝑆𝑁)

𝐴 𝐻𝑒 ( 𝑣 𝑠𝑤 , 𝑡) & SSN Present drop in 𝐴 𝐻𝑒 indicates entering minimum 25 𝜌 𝐴 𝐻𝑒 ,𝑆𝑆𝑁 peaks at 355 km/s Meaningful (>0.6) up to 488 km/s Highly significant (≥0.7) up to 426 km/s Phase offset between 𝐴 𝐻𝑒 and SSN 𝐴 𝐻𝑒 returns to same value at Max 23 & 24, even though different cycle amplitudes

Time-Lagged Cross Correlation Calculate 𝜌 𝐴 𝐻𝑒 ,𝑆𝑆𝑁 for delay times -200 days to 600 days, steps of 40 days Delay time is time for which 𝐴 𝐻𝑒 peaks as function of delay. Plot Observed (open) and Delayed (filled) 𝜌(𝑣) Error bars are repeat of procedure for 225 to 275 day averages

Time-Lagged Cross Correlation Delayed 𝜌 𝐴 𝐻𝑒 ,𝑆𝑆𝑁 ≥0.7 for all 𝑣 𝑠𝑤 Observed & Delayed 𝜌( 𝐴 𝐻𝑒 ,𝑆𝑆𝑁) peak at 355 km/s Δ𝜌 Largest in fast wind Most significant in slow wind

Phase Delay: 𝐴 𝐻𝑒 𝑆𝑆𝑁 (Top) Observed (Bottom) Delayed Hysteresis present Time is counter clock (color bar) (Bottom) Delayed Larger 𝑅 2 indicates spread of 𝐴 𝐻𝑒 about trend decreases 𝑋 𝜈 2 indicates linear model better in Delayed case As expected, fit parameters are identical.

𝜏 Delay of Peak 𝜌 𝐴 𝐻𝑒 ,𝑆𝑆𝑁 Positive delay = SSN precedes 𝐴 𝐻𝑒 Speed of instantaneous response 𝑣 𝑖 =200 km/s OR Two delays 𝜏 𝑠𝑙𝑜𝑤 =150 days 𝜏 𝑓𝑎𝑠𝑡 >300 days Either case, time lag is present

𝐴 𝐻𝑒 𝑣 𝑠𝑤 Robustness 𝐴 𝐻𝑒 𝑣 =1.62 × 10 −2 (𝑣− 𝑣 0 ) 𝐴 𝐻𝑒 SSN=0 𝐴 𝐻𝑒 𝑣 =1.62 × 10 −2 (𝑣− 𝑣 0 ) Helium vanishing speed 𝑣 0 𝑣 0 =259 km/s Kasper+ (2007), black dashed 𝐴 𝐻𝑒 SSN=0 Low solar activity 𝐴 𝐻𝑒 across Hale cycle Suitable for comparison to Kasper+ (2007)

𝐴 𝐻𝑒 𝑣 𝑠𝑤 Robustness All SSN (Unfilled) SSN<25 selects solar activity conditions similar to Min 25 𝐴 𝐻𝑒 SSN=0 Consistent in both cases Better agreement for SSN<25 Discrepancy for 𝑣 𝑠𝑤 =542 km/s expected

Helium Filtration Phase offset w/rt SSN observed in many solar indices Lyman-alpha 𝐿 𝛼 Measures chromosphere & transition region activity 125 day Soft x-ray flux (SXR) Measures active regions (ARs) > 300 day Speed-dependent phase lag suggests processes above the photosphere modify 𝐴 𝐻𝑒

Helium Filtration Two slow wind sources If two delays FIP effect Streamer belt Weak B Magnetically closed Long-lived loops ARs Strong B Higher latitudes than Streamer Belt More open flux If two delays 𝜏 𝑠𝑙𝑜𝑤 =150 days is streamer belt 𝜏 𝑓𝑎𝑠𝑡 >300 days is ARs 𝜏 reflects extent B is open FIP effect First Ionization Potential (FIP) Ion abundances differ from photospheric value Low FIP (< 10 eV) increase High FIP show apparent depletion Strongest in upper chromosphere & transition region Weakens with B Increases with loop length and age Gravitational settling interchange reconnection Not mutually exclusive